Sam has 2m + 1 individual, interchangeable white socks mixed together in his drawer. He decides to go to the store and buy 26 more pairs of white socks. When he gets back, he decides to get rid of some of the mixed socks, and throws out 16 ratty socks at the bottom of his drawer. If we disregard any socks that might be left over, how many PAIRS of socks does Sam have left after he has matched all of his socks up?

Solution:

N = (2m+1 +26-16)/2 = (2m+11)/2 = m+5 ...1

So there are (m+5) pairs of socks does Sam have left after he has matched all of his socks up